Univariate and bivariate distribution of growth traits in beef buffaloes from Brazil

The aim of this study was to analyze the weight at birth (BW) and adjusted at 205 (W205), 365 (W365) and 550 (W55O) days in beef buffaloes from Brazil, using two approaches: parametric, by normal distribution, and non-parametric, by kernel function, and thus estimating the genetic, environmental and phenotypic correlation among traits. Information of 5,169 animals at birth (BW), 3,792 at 205 days (W205), 3.883 at 365 days (W365) and 1,524 at 550 days of age (W550) were used. The birth weight distribution presented an evident discrepancy in relation to the normal distribution. However, W205, W365 and W550 presented normal distributions. The birth weight presented weak genetic, environmental, and phenotypic associations with the other weight measurements. on the other hand, the weight traits at 205, 365, 550 days of age showed a high genetic correlation.

Improved Regression Estimation of a Multivariate Relationship with Population Data on the Bivariate Relationship

Regression coefficients specify the partial effect of a regressor on the dependent variable. Sometimes the bivariate or limited multivariate relationship of that regressor variable with the dependent variable is known from population-level data. We show here that such population- level data can be used to reduce variance and bias about estimates of those regression coefficients from sample survey data. The method of constrained MLE is used to achieve these improvements. Its statistical properties are first described. The method constrains the weighted sum of all the covariate-specific associations (partial effects) of the regressors on the dependent variable to equal the overall association of one or more regressors, where the latter is known exactly from the population data. We refer to those regressors whose bivariate or limited multivariate relationships with the dependent variable are constrained by population data as being ‘‘directly constrained.’’ Our study investigates the improvements in the estimation of directly constrained variables as well as the improvements in the estimation of other regressor variables that may be correlated with the directly constrained variables, and thus ‘‘indirectly constrained’’ by the population data. The example application is to the marital fertility of black versus white women. The difference between white and black women’s rates of marital fertility, available from population-level data, gives the overall association of race with fertility. We show that the constrained MLE technique both provides a far more powerful statistical test of the partial effect of being black and purges the test of a bias that would otherwise distort the estimated magnitude of this effect. We find only trivial reductions, however, in the standard errors of the parameters for indirectly constrained regressors.

Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

The new class of Kummer beta generalized distributions

Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes. We define and study a new class of distributions called the Kummer beta generalized family to extend the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions. Some special models are discussed. The ordinary moments of any distribution in the new family can be expressed as linear functions of probability weighted moments of the baseline distribution. We examine the asymptotic distributions of the extreme values. We derive the density function of the order statistics, mean absolute deviations and entropies. We use maximum likelihood estimation to fit the distributions in the new class and illustrate its potentiality with an application to a real data set.

A Single Statistic for Monitoring the Covariance Matrix of Bivariate Processes

In this article, we present a new control chart for monitoring the covariance matrix in a bivariate process. In this method, n observations of the two variables were considered as if they came from a single variable (as a sample of 2n observations), and a sample variance was calculated. This statistic was used to build a new control chart specifically as a VMIX chart. The performance of the new control chart was compared with its main competitors: the generalized sampled variance chart, the likelihood ratio test, Nagao's test, probability integral transformation (v(t)), and the recently proposed VMAX chart. Among these statistics, only the VMAX chart was competitive with the VMIX chart. For shifts in both variances, the VMIX chart outperformed VMAX; however, VMAX showed better performance for large shifts (higher than 10%) in one variance.

A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis - latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.

Multiasset Derivatives and Joint Distributions of Asset Prices

Several of multiasset derivatives like basket options or options on the weighted maximum of assets exhibit the property that their prices determine uniquely the underlying asset distribution. Related to that the question how to retrieve this distributions from the corresponding derivatives quotes will be discussed. On the contrary, the prices of exchange options do not uniquely determine the underlying distributions of asset prices and the extent of this non-uniqueness can be characterised. The discussion is related to a geometric interpretation of multiasset derivatives as support functions of convex sets. Following this, various symmetry properties for basket, maximum and exchange options are discussed alongside with their geometric interpretations and some decomposition results for more general payoff functions.

Groundwater age distributions at a public drinking water supply well field derived from multiple age tracers (⁸⁵Kr, ³H/³He, and ³⁹Ar)

Groundwater age is a key aspect of production well vulnerability. Public drinking water supply wells typically have long screens and are expected to produce a mixture of groundwater ages. The groundwater age distributions of seven production wells of the Holten well field (Netherlands) were estimated from tritium-helium (3H/3He), krypton-85 (85Kr), and argon-39 (39Ar), using a new application of a discrete age distribution model and existing mathematical models, by minimizing the uncertainty-weighted squared differences of modeled and measured tracer concentrations. The observed tracer concentrations fitted well to a 4-bin discrete age distribution model or a dispersion model with a fraction of old groundwater. Our results show that more than 75 of the water pumped by four shallow production wells has a groundwater age of less than 20 years and these wells are very vulnerable to recent surface contamination. More than 50 of the water pumped by three deep production wells is older than 60 years. 3H/3He samples from short screened monitoring wells surrounding the well field constrained the age stratification in the aquifer. The discrepancy between the age stratification with depth and the groundwater age distribution of the production wells showed that the well field preferentially pumps from the shallow part of the aquifer. The discrete groundwater age distribution model appears to be a suitable approach in settings where the shape of the age distribution cannot be assumed to follow a simple mathematical model, such as a production well field where wells compete for capture area.

Efficient sampling from truncated bivariate Gaussians via Box-Muller transformation

Many practical simulation tasks demand procedures to draw samples efficiently from multivariate truncated Gaussian distributions. In this work, we introduce a novel rejection approach, based on the Box-Muller transformation, to generate samples from a truncated bivariate Gaussian density with an arbitrary support. Furthermore, for an important class of support regions the new method allows us to achieve exact sampling, thus becoming the most efficient approach possible. RESUMEN. Método específico para generar muestras de manera eficiente de Gaussianas bidimensionales truncadas con cualquier zona de truncamiento basado en la transformación de Box-Muller.

Flood frequency analysis by a bivariate model based on copulas

La adecuada estimación de avenidas de diseño asociadas a altos periodos de retorno es necesaria para el diseño y gestión de estructuras hidráulicas como presas. En la práctica, la estimación de estos cuantiles se realiza normalmente a través de análisis de frecuencia univariados, basados en su mayoría en el estudio de caudales punta. Sin embargo, la naturaleza de las avenidas es multivariada, siendo esencial tener en cuenta características representativas de las avenidas, tales como caudal punta, volumen y duración del hidrograma, con el fin de llevar a cabo un análisis apropiado; especialmente cuando el caudal de entrada se transforma en un caudal de salida diferente durante el proceso de laminación en un embalse o llanura de inundación. Los análisis de frecuencia de avenidas multivariados han sido tradicionalmente llevados a cabo mediante el uso de distribuciones bivariadas estándar con el fin de modelar variables correlacionadas. Sin embargo, su uso conlleva limitaciones como la necesidad de usar el mismo tipo de distribuciones marginales para todas las variables y la existencia de una relación de dependencia lineal entre ellas. Recientemente, el uso de cópulas se ha extendido en hidrología debido a sus beneficios en relación al contexto multivariado, permitiendo superar los inconvenientes de las técnicas tradicionales. Una copula es una función que representa la estructura de dependencia de las variables de estudio, y permite obtener la distribución de frecuencia multivariada de dichas variables mediante sus distribuciones marginales, sin importar el tipo de distribución marginal utilizada. La estimación de periodos de retorno multivariados, y por lo tanto, de cuantiles multivariados, también se facilita debido a la manera en la que las cópulas están formuladas. La presente tesis doctoral busca proporcionar metodologías que mejoren las técnicas tradicionales usadas por profesionales para estimar cuantiles de avenida más adecuados para el diseño y la gestión de presas, así como para la evaluación del riesgo de avenida, mediante análisis de frecuencia de avenidas bivariados basados en cópulas. Las variables consideradas para ello son el caudal punta y el volumen del hidrograma. Con el objetivo de llevar a cabo un estudio completo, la presente investigación abarca: (i) el análisis de frecuencia de avenidas local bivariado centrado en examinar y comparar los periodos de retorno teóricos basados en la probabilidad natural de ocurrencia de una avenida, con el periodo de retorno asociado al riesgo de sobrevertido de la presa bajo análisis, con el fin de proporcionar cuantiles en una estación de aforo determinada; (ii) la extensión del enfoque local al regional, proporcionando un procedimiento completo para llevar a cabo un análisis de frecuencia de avenidas regional bivariado para proporcionar cuantiles en estaciones sin aforar o para mejorar la estimación de dichos cuantiles en estaciones aforadas; (iii) el uso de cópulas para investigar tendencias bivariadas en avenidas debido al aumento de los niveles de urbanización en una cuenca; y (iv) la extensión de series de avenida observadas mediante la combinación de los beneficios de un modelo basado en cópulas y de un modelo hidrometeorológico. Accurate design flood estimates associated with high return periods are necessary to design and manage hydraulic structures such as dams. In practice, the estimate of such quantiles is usually done via univariate flood frequency analyses, mostly based on the study of peak flows. Nevertheless, the nature of floods is multivariate, being essential to consider representative flood characteristics, such as flood peak, hydrograph volume and hydrograph duration to carry out an appropriate analysis; especially when the inflow peak is transformed into a different outflow peak during the routing process in a reservoir or floodplain. Multivariate flood frequency analyses have been traditionally performed by using standard bivariate distributions to model correlated variables, yet they entail some shortcomings such as the need of using the same kind of marginal distribution for all variables and the assumption of a linear dependence relation between them. Recently, the use of copulas has been extended in hydrology because of their benefits regarding dealing with the multivariate context, as they overcome the drawbacks of the traditional approach. A copula is a function that represents the dependence structure of the studied variables, and allows obtaining the multivariate frequency distribution of them by using their marginal distributions, regardless of the kind of marginal distributions considered. The estimate of multivariate return periods, and therefore multivariate quantiles, is also facilitated by the way in which copulas are formulated. The present doctoral thesis seeks to provide methodologies that improve traditional techniques used by practitioners, in order to estimate more appropriate flood quantiles for dam design, dam management and flood risk assessment, through bivariate flood frequency analyses based on the copula approach. The flood variables considered for that goal are peak flow and hydrograph volume. In order to accomplish a complete study, the present research addresses: (i) a bivariate local flood frequency analysis focused on examining and comparing theoretical return periods based on the natural probability of occurrence of a flood, with the return period associated with the risk of dam overtopping, to estimate quantiles at a given gauged site; (ii) the extension of the local to the regional approach, supplying a complete procedure for performing a bivariate regional flood frequency analysis to either estimate quantiles at ungauged sites or improve at-site estimates at gauged sites; (iii) the use of copulas to investigate bivariate flood trends due to increasing urbanisation levels in a catchment; and (iv) the extension of observed flood series by combining the benefits of a copula-based model and a hydro-meteorological model.

Using Bird Distributions to Assess Extinction Risk and Identify Conservation Priorities in Biodiversity Hotspots

Habitat loss, fragmentation, and degradation threaten the World’s ecosystems and species. These, and other threats, will likely be exacerbated by climate change. Due to a limited budget for conservation, we are forced to prioritize a few areas over others. These places are selected based on their uniqueness and vulnerability. One of the most famous examples is the biodiversity hotspots: areas where large quantities of endemic species meet alarming rates of habitat loss. Most of these places are in the tropics, where species have smaller ranges, diversity is higher, and ecosystems are most threatened.

Species distributions are useful to understand ecological theory and evaluate extinction risk. Small-ranged species, or those endemic to one place, are more vulnerable to extinction than widely distributed species. However, current range maps often overestimate the distribution of species, including areas that are not within the suitable elevation or habitat for a species. Consequently, assessment of extinction risk using these maps could underestimate vulnerability.

In order to be effective in our quest to conserve the World’s most important places we must: 1) Translate global and national priorities into practical local actions, 2) Find synergies between biodiversity conservation and human welfare, 3) Evaluate the different dimensions of threats, in order to design effective conservation measures and prepare for future threats, and 4) Improve the methods used to evaluate species’ extinction risk and prioritize areas for conservation. The purpose of this dissertation is to address these points in Colombia and other global biodiversity hotspots.

In Chapter 2, I identified the global, strategic conservation priorities and then downscaled to practical local actions within the selected priorities in Colombia. I used existing range maps of 171 bird species to identify priority conservation areas that would protect the greatest number of species at risk in Colombia (endemic and small-ranged species). The Western Andes had the highest concentrations of such species—100 in total—but the lowest densities of national parks. I then adjusted the priorities for this region by refining these species ranges by selecting only areas of suitable elevation and remaining habitat. The estimated ranges of these species shrank by 18–100% after accounting for habitat and suitable elevation. Setting conservation priorities on the basis of currently available range maps excluded priority areas in the Western Andes and, by extension, likely elsewhere and for other taxa. By incorporating detailed maps of remaining natural habitats, I made practical recommendations for conservation actions. One recommendation was to restore forest connections to a patch of cloud forest about to become isolated from the main Andes.

For Chapter 3, I identified areas where bird conservation met ecosystem service protection in the Central Andes of Colombia. Inspired by the November 11th (2011) landslide event near Manizales, and the current poor results of Colombia’s Article 111 of Law 99 of 1993 as a conservation measure in this country, I set out to prioritize conservation and restoration areas where landslide prevention would complement bird conservation in the Central Andes. This area is one of the most biodiverse places on Earth, but also one of the most threatened. Using the case of the Rio Blanco Reserve, near Manizales, I identified areas for conservation where endemic and small-range bird diversity was high, and where landslide risk was also high. I further prioritized restoration areas by overlapping these conservation priorities with a forest cover map. Restoring forests in bare areas of high landslide risk and important bird diversity yields benefits for both biodiversity and people. I developed a simple landslide susceptibility model using slope, forest cover, aspect, and stream proximity. Using publicly available bird range maps, refined by elevation, I mapped concentrations of endemic and small-range bird species. I identified 1.54 km2 of potential restoration areas in the Rio Blanco Reserve, and 886 km2 in the Central Andes region. By prioritizing these areas, I facilitate the application of Article 111 which requires local and regional governments to invest in land purchases for the conservation of watersheds.

Chapter 4 dealt with elevational ranges of montane birds and the impact of lowland deforestation on their ranges in the Western Andes of Colombia, an important biodiversity hotspot. Using point counts and mist-nets, I surveyed six altitudinal transects spanning 2200 to 2800m. Three transects were forested from 2200 to 2800m, and three were partially deforested with forest cover only above 2400m. I compared abundance-weighted mean elevation, minimum elevation, and elevational range width. In addition to analyzing the effect of deforestation on 134 species, I tested its impact within trophic guilds and habitat preference groups. Abundance-weighted mean and minimum elevations were not significantly different between forested and partially deforested transects. Range width was marginally different: as expected, ranges were larger in forested transects. Species in different trophic guilds and habitat preference categories showed different trends. These results suggest that deforestation may affect species’ elevational ranges, even within the forest that remains. Climate change will likely exacerbate harmful impacts of deforestation on species’ elevational distributions. Future conservation strategies need to account for this by protecting connected forest tracts across a wide range of elevations.

In Chapter 5, I refine the ranges of 726 species from six biodiversity hotspots by suitable elevation and habitat. This set of 172 bird species for the Atlantic Forest, 138 for Central America, 100 for the Western Andes of Colombia, 57 for Madagascar, 102 for Sumatra, and 157 for Southeast Asia met the criteria for range size, endemism, threat, and forest use. Of these 586 species, the Red List deems 108 to be threatened: 15 critically endangered, 29 endangered, and 64 vulnerable. When ranges are refined by elevational limits and remaining forest cover, 10 of those critically endangered species have ranges < 100km2, but then so do 2 endangered species, seven vulnerable, and eight non-threatened ones. Similarly, 4 critically endangered species, 20 endangered, and 12 vulnerable species have refined ranges < 5000km2, but so do 66 non-threatened species. A striking 89% of these species I have classified in higher threat categories have <50% of their refined ranges inside protected areas. I find that for 43% of the species I assessed, refined range sizes fall within thresholds that typically have higher threat categories than their current assignments. I recommend these species for closer inspection by those who assess risk. These assessments are not only important on a species-by-species basis, but by combining distributions of threatened species, I create maps of conservation priorities. They differ significantly from those created from unrefined ranges.

Sociodemographic factors influencing adherence to antenatal iron supplementation recommendations among pregnant women in Malawi: Analysis of data from the 2010 Malawi Demographic and Health Survey

Background and Aim: Maternal morbidity and mortality statistics remain unacceptably high in Malawi. Prominent among the risk factors in the country is anaemia in pregnancy, which generally results from nutritional inadequacy (particularly iron deficiency) and malaria, among other factors. This warrants concerted efforts to increase iron intake among reproductive-age women. This study, among women in Malawi, examined factors determining intake of supplemental iron for at least 90 days during pregnancy. Methods: A weighted sample of 10,750 women (46.7%), from the 23,020 respondents of the 2010 Malawi Demographic and Health Survey (MDHS), were utilized for the study. Univariate, bivariate, and regression techniques were employed. While univariate analysis revealed the percent distributions of all variables, bivariate analysis was used to examine the relationships between individual independent variables and adherence to iron supplementation. Chi-square tests of independence were conducted for categorical variables, with the significance level set at P < 0.05. Two binary logistic regression models were used to evaluate the net effect of independent variables on iron supplementation adherence. Results: Thirty-seven percent of the women adhered to the iron supplementation recommendations during pregnancy. Multivariate analysis indicated that younger age, urban residence, higher education, higher wealth status, and attending antenatal care during the first trimester were significantly associated with increased odds of taking iron supplementation for 90 days or more during pregnancy (P < 0.01). Conclusions: The results indicate low adherence to the World Health Organization’s iron supplementation recommendations among pregnant women in Malawi, and this contributes to negative health outcomes for both mothers and children. Focusing on education interventions that target populations with low rates of iron supplement intake, including campaigns to increase the number of women who attend antenatal care clinics in the first trimester, are recommended to increase adherence to iron supplementation recommendations.

BIAS-CORRECTED MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF THE WEIGHTED LINDLEY DISTRIBUTION

This report discusses the calculation of analytic second-order bias techniques for the maximum likelihood estimates (for short, MLEs) of the unknown parameters of the distribution in quality and reliability analysis. It is well-known that the MLEs are widely used to estimate the unknown parameters of the probability distributions due to their various desirable properties; for example, the MLEs are asymptotically unbiased, consistent, and asymptotically normal. However, many of these properties depend on an extremely large sample sizes. Those properties, such as unbiasedness, may not be valid for small or even moderate sample sizes, which are more practical in real data applications. Therefore, some bias-corrected techniques for the MLEs are desired in practice, especially when the sample size is small. Two commonly used popular techniques to reduce the bias of the MLEs, are ‘preventive’ and ‘corrective’ approaches. They both can reduce the bias of the MLEs to order O(n−2), whereas the ‘preventive’ approach does not have an explicit closed form expression. Consequently, we mainly focus on the ‘corrective’ approach in this report. To illustrate the importance of the bias-correction in practice, we apply the bias-corrected method to two popular lifetime distributions: the inverse Lindley distribution and the weighted Lindley distribution. Numerical studies based on the two distributions show that the considered bias-corrected technique is highly recommended over other commonly used estimators without bias-correction. Therefore, special attention should be paid when we estimate the unknown parameters of the probability distributions under the scenario in which the sample size is small or moderate.